All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons

TL;DR

This paper derives all exact solutions for non-Abelian vortices in a specific gauge theory by connecting them to Yang-Mills instantons, providing a comprehensive understanding of their moduli space.

Contribution

It introduces the first complete set of exact non-Abelian vortex solutions and establishes the ADHM construction for these vortices.

Findings

Derived all exact solutions of non-Abelian vortices.

Identified the full moduli space and parameters.

Connected vortex solutions to Yang-Mills instantons.

Abstract

We successfully exhaust the complete set of exact solutions of non-Abelian vortices in a quiver gauge theory, that is, the S[U(N) x U(N)] gauge theory with a bi-fudamental scalar field on a hyperbolic plane with a certain curvature, from SO(3)-invariant SU(2N) Yang-Mills instanton solutions. This work provides, for the first time, exact non-Abelian vortex solutions. We establish the ADHM construction for non-Abelian vortices and identify all the moduli parameters and the complete moduli space.